Introduction to Cryptography with Open-Source Software

Public-key cryptosystems based on factoring 103

sage: join(ms,’’)

’Withdraw one hundred dollars’

It will be convenient to put these commands into functions str2num and

num2str which translates a string into a single integer, and back again:

def str2num(s):

return ZZ(map(ord,s),256)

def num2str(n):

nl=n.digits(256)

return join(map(chr,nl),’’)

Now to demonstrate RSA with some non-trivia lly small integers first create

some large primes:

sage: p = next_prime(2^330)

sage: p

2187250724783011924372502227117621365353169430893212436425770

606409952999199375923223513177023053917

sage: q = next_prime(3^210)

sage: q

1568424042913152925468569828489075118463940614573029159280267 ...